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International Mathematics Research Notices (2007) Vol. 2007 : article ID rnm077, 21 pages, doi:10.1093/imrn/rnm077 published on September 19, 2007
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Copyright © The Author 2007. Published by Oxford University Press.

A Concordance Invariant from the Floer Homology of Double Branched Covers

Ciprian Manolescu1, and Brendan Owens2

1 Department of Mathematics, Columbia University New York, NY 10027, USA
2 Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA

Correspondence: Correspondence to be sent to: Ciprian Manolescu, Department of Mathematics, Columbia University New York, NY 10027, USA. e-mail: cm{at}math.columbia.edu

Ozsváth and Szabó defined an analog of the Frøyshov invariant in the form of a correction term for the grading in Heegaard Floer homology. Applying this to the double cover of the 3-sphere branched over a knot K, we obtain an invariant {delta} of knot concordance. We show that {delta} is determined by the signature for alternating knots and knots with up to nine crossings, and conjecture a similar relation for all H-thin knots. We also use {delta} to prove that for all knots K with {tau}(K) > 0, the positive untwisted double of K is not smoothly slice.

Communicated by Yasha Eliashberg


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